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Simplifying 12x2 + -12x + 1 = 34 Reorder the terms: 1 + -12x + 12x2 = 34 Solving 1 + -12x + 12x2 = 34 Solving for variable 'x'. Reorder the terms: 1 + -34 + -12x + 12x2 = 34 + -34 Combine like terms: 1 + -34 = -33 -33 + -12x + 12x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -33 + -12x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + -4x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -4x + 4x2)' equal to zero and attempt to solve: Simplifying -11 + -4x + 4x2 = 0 Solving -11 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -1x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -1x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -1x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -1x + x2 = 0 + 2.75 -1x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -1x + x2 = 2.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.75 + 0.25 Combine like terms: 2.75 + 0.25 = 3 0.25 + -1x + x2 = 3 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -0.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -0.5 = 1.732050808 Simplifying x + -0.5 = 1.732050808 Reorder the terms: -0.5 + x = 1.732050808 Solving -0.5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.732050808 + 0.5 x = 1.732050808 + 0.5 Combine like terms: 1.732050808 + 0.5 = 2.232050808 x = 2.232050808 Simplifying x = 2.232050808Subproblem 2
x + -0.5 = -1.732050808 Simplifying x + -0.5 = -1.732050808 Reorder the terms: -0.5 + x = -1.732050808 Solving -0.5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.732050808 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.732050808 + 0.5 x = -1.732050808 + 0.5 Combine like terms: -1.732050808 + 0.5 = -1.232050808 x = -1.232050808 Simplifying x = -1.232050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.232050808, -1.232050808}Solution
x = {2.232050808, -1.232050808}
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